Related papers: Market Pricing for Matroid Rank Valuations
The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Under truthful bidding, the SMRA is known to output a Walrasian equilibrium that maximizes…
This paper aims to investigate how a central authority (e.g. a government) can increase social welfare in a network of markets and firms. In these networks, modeled using a bipartite graph, firms compete with each other \textit{\`a la}…
In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous…
Fairness and efficiency have become the pillars of modern fair division research, but prior work on achieving both simultaneously is largely limited to the unconstrained setting. We study fair and efficient allocations of indivisible goods…
This paper is merged with arXiv:2107.08965v2. We refer the reader to the full and updated version. We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an…
We consider combinatorial multi-item markets and propose the notion of a $\Delta$-regret Walras equilibrium, which is an allocation of items to players and a set of item prices that achieve the following goals: prices clear the market, the…
We consider the problem of posting prices for unit-demand buyers if all $n$ buyers have identically distributed valuations drawn from a distribution with monotone hazard rate. We show that even with multiple items asymptotically optimal…
Motivated by the success of the serial dictatorship mechanism in social choice settings, we explore its usefulness in tackling various combinatorial optimization problems. We do so by considering an abstract model, in which a set of agents…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed…
We consider dynamic auctions for finding Walrasian equilibria in markets with indivisible items and strong gross substitutes valuation functions. Each price adjustment step in these auction algorithms requires finding an inclusion-wise…
We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a…
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…
We provide optimal solutions to an institution that has distributional objectives when choosing from a set of applications based on merit (or priority). For example, in college admissions, administrators may want to admit a diverse class in…
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The…
We study algorithms for combinatorial market design problems, where a set of heterogeneous and indivisible objects are priced and sold to potential buyers subject to equilibrium constraints. Extending the CWE notion introduced by Feldman et…
Bi-objective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. However, if one of the objective functions is restricted to binary cost coefficients the problem…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
We study the efficiency of allocations in large markets with a network structure where every seller owns an edge in a graph and every buyer desires a path connecting some nodes. While it is known that stable allocations in such settings can…
We study fair allocation of indivisible goods when agents have matroid rank valuations. Our main contribution is a simple algorithm based on the colloquial Yankee Swap procedure that computes provably fair and efficient Lorenz dominating…